Robust Petri Net Controllers for Flexible Manufacturing Systems With Multitype and Multiunit Unreliable Resources

Abstract

It is inevitable that resource failures occur in real production processes, and sometimes many different types of unreliable resource failures may occur. Once there are resource failures, the stagnation states of production caused by these failures, called as failure blockings (FBs), tend to appear. Hence, both deadlocks and FBs can arise to reduce production efficiency sharply. Designing robust control policies for such an automated system is thus very important. Our work focuses on a novel robust Petri net controller of flexible manufacturing systems with multitype and multiunit of unreliable resources. First, under the assumption that all resources are reliable, these systems are modeled by a class of Petri nets called systems of simple sequential processes with resources (S3PRs). For each operation place that is a holder of an unreliable resource, the corresponding repair place and related transitions are added to the net and an S3PR with unreliable resources (S3PRu) is developed. For an S3PRu, the formal definition of FBs is then proposed. Such an FB is characterized by a maximal perfect resource-transition circuit (MPC). Next, the concept of a critical set of MPCs is introduced. For any two adjacent MPCs in such a critical set, one input transition of the former and one output transition of the latter are connected by passing through resource places. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resource is a one-unit resource shared by two or more MPCs that do not contain each other. For an S3PRu without <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources and critical sets of MPCs, a control place corresponding to an MPC is added to the net with its output arcs to the input transitions of the MPC. However, for an S3PRu with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources or critical sets of MPCs, the output arcs of each control place are added to the source transitions of the original net. Thus, a novel robust controller of an S3PRu is synthesized. Such a robust controller can guarantee that as long as at least one unit of each type of unreliable resources can work normally, all kinds of parts can be processed to complete smoothly their tasks through any one of their process routes. Finally, three examples are provided to illustrate the efficiency of the proposed robust controller.